securities to stabilize income. The various revenue$-$producing investments together with annual rates of return are as follows.

$\backslash$table$[[$Type of Loan$/$Investment$,$Annual Rate of Return $(\%)],[$Automobile loans,$9],[$Furniture loans,$11],[$Other secured loans,$12],[$Signature loans,$13],[$Risk$-$free securities$,10]]$

Risk$-$free securities may not exceed $30\%$ of the total funds available for investment.

Signature loans may not exceed $10\%$ of the funds invested in all loans $($automobile$,$ furniture, other secured, and signature loans$).$

Furniture loans plus other secured loans may not exceed the automobile loans.

Other secured loans plus signature loans may not exceed the funds invested in risk$-$free securities$.$

How should the $$2,400,000$ be allocated to each of the loan$/$investment alternatives to maximize total annual return?

$\backslash$table$[[$Automobile loans,$